Three-dimensional topological photonic crystal with a single surface Dirac cone

TL;DR

This paper predicts a 3D photonic crystal with a single, robust surface Dirac cone protected by nonsymmorphic symmetry and broken time-reversal symmetry, representing a bosonic topological insulator analog.

Contribution

It introduces a novel 3D photonic crystal design exhibiting a single surface Dirac cone protected by nonsymmorphic symmetry, a first in bosonic topological systems.

Findings

Single Dirac cone surface state predicted

Surface state protected by nonsymmorphic glide reflection

Achieved via applying alternating magnetization

Abstract

A single Dirac cone on the surface is the hallmark of three-dimensional (3D) topological insulators, where the double degeneracy at the Dirac point is protected by time-reversal symmetry and the spin-splitting away from the point is provided by the spin-orbital coupling. Here we predict a single Dirac-cone surface state in a 3D photonic crystal, where the degeneracy at the Dirac point is protected by a nonsymmorphic glide reflection and the linear splitting away from it is enabled by breaking time-reversal symmetry. Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D "generalized Dirac points" discovered in the bulk of our crystal. The $Z_2$ bulk invariant is characterized through the evolution of Wannier centers. Our proposal--readily realizable using ferrimagnetic materials at microwave frequencies--can also be regarded as the photonic analog of topological crystalline insulators, providing the first 3D bosonic symmetry-protected topological system.